Joelle had 462 pencils. ²₇ were green and the rest were pink and gold. The ratio of the number of pink pencils to the number of gold pencils was 1 : 5. Joelle decided to buy some more green pencils to increase the number of green pencils to half of the total number of pencils.

1. How many less pink pencils than green pencils did he have at first?
2. How many more green pencils did he have to buy?

Green pencils	Pink pencils	Gold pencils	Total
2x6	5x6
	1x5	5x5
12 u	5 u	25 u	462

	Green pencils	Pink pencils	Gold pencils
Before	12 u	5 u	25 u
Change	+ ?
After	30 u	30 u
Comparing green, pink and gold pencils in the end	1	1

(a)
The total number of pink pencils and gold pencils is repeated. Make the total number of pink pencils and gold pencils the same.  LCM of 5 and 6 is 30.

Total number of pencils at first
= 12 u + 5 u + 25 u
= 42 u

42 u = 462

1 u = 462 ÷ 42 = 11

Number of less pink pencils than green pencils at first
= 12 u - 5 u
= 7 u
= 7 x 11
= 77

(b)
Number of more green pencils that Joelle had to buy
= 30 u - 12 u
= 18 u
= 18 x 11
= 198

Answer(s): (a) 77; (b) 198